Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719224 | C2 | semidirect |
| 3. C13×#424 | C2 | semidirect |
| 5. #11718782 | C2 | semidirect |
| 7. C2×#88057 | C2 | semidirect |
| 8. #11718512 | C2 | semidirect |
| 9. #11718508 | C2 | semidirect |
| 10. #11718503 | C2 | semidirect |
| 11. #11718490 | C2 | semidirect |
| 46. #6127 | Q8 | semidirect |
| 110. #424 | D13 | semidirect |
| 198. C13 | #3084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719228 | 2 |
| #11719224 | 2 |
| C13×#424 | 2 |
| #11718794 | 2 |
| #11718782 | 2 |
| #11718774 | 2 |
| C2×#88057 | 2 |
| #11718512 | 2 |
| #11718508 | 2 |
| #11718503 | 2 |
| #11718490 | 2 |
| #3084 | 13 |